Polytope of Type {12,12}

Play with this polytope as a twisty puzzle

This page is part of the Atlas of Small Regular Polytopes
Atlas Canonical Name : {12,12}*1152l
if this polytope has a name.
Group : SmallGroup(1152,156063)
Rank : 3
Schlafli Type : {12,12}
Number of vertices, edges, etc : 48, 288, 48
Order of s0s1s2 : 12
Order of s0s1s2s1 : 6
Special Properties :
   Compact Hyperbolic Quotient
   Locally Spherical
   Orientable
Related Polytopes :
   Facet
   Vertex Figure
   Dual
   Petrial
Facet Of :
   None in this Atlas
Vertex Figure Of :
   None in this Atlas
Quotients (Maximal Quotients in Boldface) :
   2-fold quotients : {12,6}*576a, {6,12}*576e
   3-fold quotients : {12,12}*384a
   4-fold quotients : {12,12}*288c, {6,6}*288b
   6-fold quotients : {6,12}*192a, {12,6}*192a
   8-fold quotients : {12,6}*144b, {6,12}*144c, {3,6}*144
   12-fold quotients : {12,4}*96a, {6,6}*96
   16-fold quotients : {6,6}*72c
   24-fold quotients : {12,2}*48, {6,4}*48a, {3,6}*48, {6,3}*48
   32-fold quotients : {3,6}*36
   36-fold quotients : {4,4}*32
   48-fold quotients : {3,3}*24, {6,2}*24
   72-fold quotients : {2,4}*16, {4,2}*16
   96-fold quotients : {3,2}*12
   144-fold quotients : {2,2}*8
Covers (Minimal Covers in Boldface) :
   None in this atlas.
Irregular Quotients (of which this is a minimal cover):
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s2*s1*s2> of order 2.
      24 facets:
         24 of {12}*24
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2> of order 2.
      24 facets:
         24 of {12}*24
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s2*s1*s0*s2*s1*s2> of order 2.
      24 facets:
         24 of {12}*24
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s1*s0*s1*s2*s1*s2*s1*s2*s1*s0*s1*s2> of order 2.
      24 facets:
         24 of {12}*24
      24 vertex figures:
         24 of {12}*24
   P/N, where N=<s0*s2*s1*s2*s1*s0*s1*s2*s1*s2> of order 3.
      16 facets:
         16 of {12}*24
      24 vertex figures:
         12 of {12}*24
         12 of {4}*8
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s2*s1*s2, s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1> of order 4.
      12 facets:
         12 of {12}*24
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s0> of order 4.
      12 facets:
         12 of {12}*24
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s1*s2*s1*s2*s1*s2*s1, s0*s1*s0*s1*s0*s2*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2> of order 4.
      12 facets:
         12 of {12}*24
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1> of order 4.
      12 facets:
         12 of {12}*24
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s0*s2*s1*s0*s1*s2> of order 4.
      12 facets:
         12 of {12}*24
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s0*s1*s2*s1*s0*s2*s1*s2*s1> of order 4.
      12 facets:
         12 of {12}*24
      12 vertex figures:
         12 of {12}*24
   P/N, where N=<s1*s0*s2*s1*s2*s1*s0*s2*s1*s2, s0*s1*s0*s1*s0*s1*s0*s1*s0*s2*s1*s0*s2*s1*s2*s1*s2*s1> of order 4.
      12 facets:
         12 of {12}*24
      12 vertex figures:
         12 of {12}*24

Permutation Representation (GAP) : 
s0 := (  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 69)( 54, 70)( 55, 72)( 56, 71)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)( 85, 97)( 86, 98)( 87,100)( 88, 99)( 89,105)( 90,106)( 91,108)( 92,107)( 93,101)( 94,102)( 95,104)( 96,103)(111,112)(113,117)(114,118)(115,120)(116,119)(121,133)(122,134)(123,136)(124,135)(125,141)(126,142)(127,144)(128,143)(129,137)(130,138)(131,140)(132,139)(145,253)(146,254)(147,256)(148,255)(149,261)(150,262)(151,264)(152,263)(153,257)(154,258)(155,260)(156,259)(157,277)(158,278)(159,280)(160,279)(161,285)(162,286)(163,288)(164,287)(165,281)(166,282)(167,284)(168,283)(169,265)(170,266)(171,268)(172,267)(173,273)(174,274)(175,276)(176,275)(177,269)(178,270)(179,272)(180,271)(181,217)(182,218)(183,220)(184,219)(185,225)(186,226)(187,228)(188,227)(189,221)(190,222)(191,224)(192,223)(193,241)(194,242)(195,244)(196,243)(197,249)(198,250)(199,252)(200,251)(201,245)(202,246)(203,248)(204,247)(205,229)(206,230)(207,232)(208,231)(209,237)(210,238)(211,240)(212,239)(213,233)(214,234)(215,236)(216,235);;
s1 := (  1,161)(  2,164)(  3,163)(  4,162)(  5,157)(  6,160)(  7,159)(  8,158)(  9,165)( 10,168)( 11,167)( 12,166)( 13,149)( 14,152)( 15,151)( 16,150)( 17,145)( 18,148)( 19,147)( 20,146)( 21,153)( 22,156)( 23,155)( 24,154)( 25,173)( 26,176)( 27,175)( 28,174)( 29,169)( 30,172)( 31,171)( 32,170)( 33,177)( 34,180)( 35,179)( 36,178)( 37,197)( 38,200)( 39,199)( 40,198)( 41,193)( 42,196)( 43,195)( 44,194)( 45,201)( 46,204)( 47,203)( 48,202)( 49,185)( 50,188)( 51,187)( 52,186)( 53,181)( 54,184)( 55,183)( 56,182)( 57,189)( 58,192)( 59,191)( 60,190)( 61,209)( 62,212)( 63,211)( 64,210)( 65,205)( 66,208)( 67,207)( 68,206)( 69,213)( 70,216)( 71,215)( 72,214)( 73,233)( 74,236)( 75,235)( 76,234)( 77,229)( 78,232)( 79,231)( 80,230)( 81,237)( 82,240)( 83,239)( 84,238)( 85,221)( 86,224)( 87,223)( 88,222)( 89,217)( 90,220)( 91,219)( 92,218)( 93,225)( 94,228)( 95,227)( 96,226)( 97,245)( 98,248)( 99,247)(100,246)(101,241)(102,244)(103,243)(104,242)(105,249)(106,252)(107,251)(108,250)(109,269)(110,272)(111,271)(112,270)(113,265)(114,268)(115,267)(116,266)(117,273)(118,276)(119,275)(120,274)(121,257)(122,260)(123,259)(124,258)(125,253)(126,256)(127,255)(128,254)(129,261)(130,264)(131,263)(132,262)(133,281)(134,284)(135,283)(136,282)(137,277)(138,280)(139,279)(140,278)(141,285)(142,288)(143,287)(144,286);;
s2 := (  1,  2)(  5,  6)(  9, 10)( 13, 26)( 14, 25)( 15, 27)( 16, 28)( 17, 30)( 18, 29)( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 23, 35)( 24, 36)( 37, 38)( 41, 42)( 45, 46)( 49, 62)( 50, 61)( 51, 63)( 52, 64)( 53, 66)( 54, 65)( 55, 67)( 56, 68)( 57, 70)( 58, 69)( 59, 71)( 60, 72)( 73, 74)( 77, 78)( 81, 82)( 85, 98)( 86, 97)( 87, 99)( 88,100)( 89,102)( 90,101)( 91,103)( 92,104)( 93,106)( 94,105)( 95,107)( 96,108)(109,110)(113,114)(117,118)(121,134)(122,133)(123,135)(124,136)(125,138)(126,137)(127,139)(128,140)(129,142)(130,141)(131,143)(132,144)(145,218)(146,217)(147,219)(148,220)(149,222)(150,221)(151,223)(152,224)(153,226)(154,225)(155,227)(156,228)(157,242)(158,241)(159,243)(160,244)(161,246)(162,245)(163,247)(164,248)(165,250)(166,249)(167,251)(168,252)(169,230)(170,229)(171,231)(172,232)(173,234)(174,233)(175,235)(176,236)(177,238)(178,237)(179,239)(180,240)(181,254)(182,253)(183,255)(184,256)(185,258)(186,257)(187,259)(188,260)(189,262)(190,261)(191,263)(192,264)(193,278)(194,277)(195,279)(196,280)(197,282)(198,281)(199,283)(200,284)(201,286)(202,285)(203,287)(204,288)(205,266)(206,265)(207,267)(208,268)(209,270)(210,269)(211,271)(212,272)(213,274)(214,273)(215,275)(216,276);;
poly := Group([s0,s1,s2]);;
Finitely Presented Group Representation (GAP) : 
F := FreeGroup("s0","s1","s2");;
s0 := F.1;;  s1 := F.2;;  s2 := F.3;;  
rels := [ s0*s0, s1*s1, s2*s2, s0*s2*s0*s2, s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 ];;
poly := F / rels;;
Permutation Representation (Magma) : 
s0 := Sym(288)!(  3,  4)(  5,  9)(  6, 10)(  7, 12)(  8, 11)( 13, 25)( 14, 26)( 15, 28)( 16, 27)( 17, 33)( 18, 34)( 19, 36)( 20, 35)( 21, 29)( 22, 30)( 23, 32)( 24, 31)( 39, 40)( 41, 45)( 42, 46)( 43, 48)( 44, 47)( 49, 61)( 50, 62)( 51, 64)( 52, 63)( 53, 69)( 54, 70)( 55, 72)( 56, 71)( 57, 65)( 58, 66)( 59, 68)( 60, 67)( 75, 76)( 77, 81)( 78, 82)( 79, 84)( 80, 83)( 85, 97)( 86, 98)( 87,100)( 88, 99)( 89,105)( 90,106)( 91,108)( 92,107)( 93,101)( 94,102)( 95,104)( 96,103)(111,112)(113,117)(114,118)(115,120)(116,119)(121,133)(122,134)(123,136)(124,135)(125,141)(126,142)(127,144)(128,143)(129,137)(130,138)(131,140)(132,139)(145,253)(146,254)(147,256)(148,255)(149,261)(150,262)(151,264)(152,263)(153,257)(154,258)(155,260)(156,259)(157,277)(158,278)(159,280)(160,279)(161,285)(162,286)(163,288)(164,287)(165,281)(166,282)(167,284)(168,283)(169,265)(170,266)(171,268)(172,267)(173,273)(174,274)(175,276)(176,275)(177,269)(178,270)(179,272)(180,271)(181,217)(182,218)(183,220)(184,219)(185,225)(186,226)(187,228)(188,227)(189,221)(190,222)(191,224)(192,223)(193,241)(194,242)(195,244)(196,243)(197,249)(198,250)(199,252)(200,251)(201,245)(202,246)(203,248)(204,247)(205,229)(206,230)(207,232)(208,231)(209,237)(210,238)(211,240)(212,239)(213,233)(214,234)(215,236)(216,235);
s1 := Sym(288)!(  1,161)(  2,164)(  3,163)(  4,162)(  5,157)(  6,160)(  7,159)(  8,158)(  9,165)( 10,168)( 11,167)( 12,166)( 13,149)( 14,152)( 15,151)( 16,150)( 17,145)( 18,148)( 19,147)( 20,146)( 21,153)( 22,156)( 23,155)( 24,154)( 25,173)( 26,176)( 27,175)( 28,174)( 29,169)( 30,172)( 31,171)( 32,170)( 33,177)( 34,180)( 35,179)( 36,178)( 37,197)( 38,200)( 39,199)( 40,198)( 41,193)( 42,196)( 43,195)( 44,194)( 45,201)( 46,204)( 47,203)( 48,202)( 49,185)( 50,188)( 51,187)( 52,186)( 53,181)( 54,184)( 55,183)( 56,182)( 57,189)( 58,192)( 59,191)( 60,190)( 61,209)( 62,212)( 63,211)( 64,210)( 65,205)( 66,208)( 67,207)( 68,206)( 69,213)( 70,216)( 71,215)( 72,214)( 73,233)( 74,236)( 75,235)( 76,234)( 77,229)( 78,232)( 79,231)( 80,230)( 81,237)( 82,240)( 83,239)( 84,238)( 85,221)( 86,224)( 87,223)( 88,222)( 89,217)( 90,220)( 91,219)( 92,218)( 93,225)( 94,228)( 95,227)( 96,226)( 97,245)( 98,248)( 99,247)(100,246)(101,241)(102,244)(103,243)(104,242)(105,249)(106,252)(107,251)(108,250)(109,269)(110,272)(111,271)(112,270)(113,265)(114,268)(115,267)(116,266)(117,273)(118,276)(119,275)(120,274)(121,257)(122,260)(123,259)(124,258)(125,253)(126,256)(127,255)(128,254)(129,261)(130,264)(131,263)(132,262)(133,281)(134,284)(135,283)(136,282)(137,277)(138,280)(139,279)(140,278)(141,285)(142,288)(143,287)(144,286);
s2 := Sym(288)!(  1,  2)(  5,  6)(  9, 10)( 13, 26)( 14, 25)( 15, 27)( 16, 28)( 17, 30)( 18, 29)( 19, 31)( 20, 32)( 21, 34)( 22, 33)( 23, 35)( 24, 36)( 37, 38)( 41, 42)( 45, 46)( 49, 62)( 50, 61)( 51, 63)( 52, 64)( 53, 66)( 54, 65)( 55, 67)( 56, 68)( 57, 70)( 58, 69)( 59, 71)( 60, 72)( 73, 74)( 77, 78)( 81, 82)( 85, 98)( 86, 97)( 87, 99)( 88,100)( 89,102)( 90,101)( 91,103)( 92,104)( 93,106)( 94,105)( 95,107)( 96,108)(109,110)(113,114)(117,118)(121,134)(122,133)(123,135)(124,136)(125,138)(126,137)(127,139)(128,140)(129,142)(130,141)(131,143)(132,144)(145,218)(146,217)(147,219)(148,220)(149,222)(150,221)(151,223)(152,224)(153,226)(154,225)(155,227)(156,228)(157,242)(158,241)(159,243)(160,244)(161,246)(162,245)(163,247)(164,248)(165,250)(166,249)(167,251)(168,252)(169,230)(170,229)(171,231)(172,232)(173,234)(174,233)(175,235)(176,236)(177,238)(178,237)(179,239)(180,240)(181,254)(182,253)(183,255)(184,256)(185,258)(186,257)(187,259)(188,260)(189,262)(190,261)(191,263)(192,264)(193,278)(194,277)(195,279)(196,280)(197,282)(198,281)(199,283)(200,284)(201,286)(202,285)(203,287)(204,288)(205,266)(206,265)(207,267)(208,268)(209,270)(210,269)(211,271)(212,272)(213,274)(214,273)(215,275)(216,276);
poly := sub<Sym(288)|s0,s1,s2>;
Finitely Presented Group Representation (Magma) : 
poly<s0,s1,s2> := Group< s0,s1,s2 | s0*s0, s1*s1, s2*s2, 
s0*s2*s0*s2, s0*s1*s0*s1*s2*s1*s2*s0*s1*s0*s1*s0*s1*s2*s1*s2*s0*s1, 
s0*s1*s2*s0*s1*s2*s1*s2*s1*s2*s1*s2*s0*s1*s0*s1*s2*s1, 
s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1*s2*s0*s1*s2*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1, 
s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1*s0*s1*s0*s1*s0*s1*s0*s1*s0*s1*s2*s1 >;
References : None.
to this polytope

Twisty Puzzle